Solar, it is not enough to just assign the same workspace. The other key items are:

What have you set your Color Management Policies to in PS Color Settings? These determine how PS treats files with embedded profiles. If your settings are check to automatically ignore the profile or convert to the working color space, then you can easily do something that you don't really want. It is a good idea to check off the Advanced options so that PS will always ask you if you want to convert or ignore or assign a profile to an untagged file. I am not familiar with PSP but I assume that program has similar color management policies.
The other thing people often miss is the check box to embed the profile in the File>Save As dialog box.
Bottom line - If the color conversion engines in both applications are set to properly respect a particular color profile and if that profile is properly embedded in the file, the image should look identical in both programs on the same monitor.
Regards, Murray